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Statistical Optimal Control Using Neural Networks

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Advances in Neural Networks – ISNN 2011 (ISNN 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6676))

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Abstract

In this paper, we investigated statistical control problems using n-th order cost cumulants. The n-th order statistical control is formulated and solved using a Hamilton-Jacobi-Bellman (HJB) partial differential equation. Both necessary and sufficient conditions for n-th cumulant statistical control are derived. Statistical control introduces an extra degree of freedom to improve the performance. Then, the neural network approximation method is applied to solve the HJB equation numerically. This gives a statistical optimal controller. We apply statistical optimal control to a satellite attitude control application. This illustrates that neural network is useful in solving an n-th cumulant HJB equation, and the statistical controller improves the system performance.

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Author information

Authors and Affiliations

  1. College of Engineering, CSNAP Laboratory, 1947 N. 12th Street, Philadelphia, PA, 19122, USA

    Bei Kang & Chang-Hee Won

Authors
  1. Bei Kang
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  2. Chang-Hee Won
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Editor information

Editors and Affiliations

  1. Institute of Automation, Key Laboratory of Complex Systems and Intelligence Science, Chinese Academy of Sciences, 100190, Beijing, China

    Derong Liu

  2. College of Information Science and Engineering, Northeastern University, 110004, Shenyang, Liaoing, China

    Huaguang Zhang

  3. Department of Electrical and Computer Engineering, University of Cyprus, 75 Kallipoleos Avenue, 1678, Nicosia, Cyprus

    Marios Polycarpou

  4. Dipartimento di Elettronica, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italy

    Cesare Alippi

  5. Deptartment of Electrical, Computer and Biomedical Engineering, University of Rhode Island, 02881, Kingston, RI, USA

    Haibo He

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© 2011 Springer-Verlag Berlin Heidelberg

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Kang, B., Won, CH. (2011). Statistical Optimal Control Using Neural Networks. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21090-7_69

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  • DOI: https://doi.org/10.1007/978-3-642-21090-7_69

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21089-1

  • Online ISBN: 978-3-642-21090-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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